IDZ 2.1 - Option 21. Decisions Ryabushko AP

1. Given the vectors a = αm + βn and b = γm + δn, where | m | = k; | n | = l; (m, ^ n) = φ.
  Find a) (λa + μb) ∙ (νa + τb); b) PRV (νa + τb); a) cos (a, ^ τb)
  1.21 α = -5, β = -6, γ = 2, δ = 7, k = 2, l = 7, φ = π, λ = -2, μ = 5, ν = 1, τ = 3

  2. The coordinates of points A, B and C for the indicated vectors to find: a) a unit vector; b) the inner product of vectors a and b; c) the projection of c-vector d; z) coordinates of the point M, dividing the segment l against α: β
  2.21 A (3, 4, 6), B (-4, 6, 4), C (5, -2, -3) a = -7BC + 4CA, b = BA, c = CA, d = BC, l = BA, α = 5, β = 3

  3. Prove that the vectors a, b, c form a basis, and to find the coordinates of the vector d in this basis.
  3.21 a (9, 5, 3); b (-3, 2, 1); c (4, -7, 4); d (-10, -13, 8)